In the given circuit,the peak voltages across $C$,$L$,and $R$ are $30 \,V$,$110 \,V$,and $60 \,V$,respectively. The rms value of the applied voltage is (in $\,V$)

$A$ $50 \,W$ bulb connected in series with a heater coil is put to an $AC$ mains. Now the bulb is replaced by a $100 \,W$ bulb. The heater output will ...........

$A$ sinusoidal voltage of peak value $283 \;V$ and frequency $50 \;Hz$ is applied to a series $LCR$ circuit in which $R = 3 \;\Omega, L = 25.48 \;mH,$ and $C = 796 \;\mu F.$ Find
$(a)$ the impedance of the circuit;
$(b)$ the phase difference between the voltage across the source and the current;
$(c)$ the power dissipated in the circuit; and
$(d)$ the power factor.

In a series $LCR$ circuit,the resistance is $18 \ \Omega$ and the impedance is $33 \ \Omega$. An $r.m.s.$ voltage of $220 \ V$ is applied across the circuit. The true power consumed in the $a.c.$ circuit is: (in $W$)

$A$ sinusoidal voltage with a frequency of $50 \ Hz$ is applied to a series $LCR$ circuit with a resistance of $5 \ \Omega$,inductance of $20 \ mH$ and a capacitance of $500 \ \mu F$. The magnitude of impedance of the circuit is close to (in $\Omega$)

An inductor of reactance $100 \text{ } \Omega$, a capacitor of reactance $50 \text{ } \Omega$, and a resistor of resistance $50 \text{ } \Omega$ are connected in series with an $AC$ source of $10 \text{ V}$, $50 \text{ Hz}$. Average power dissipated by the circuit is (in $\text{ W}$)